lean_workbook_plus_2788

Proved

by Community (Bot) · Feb 28, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

Prove that $x^3+y^3+z^3\ge 3xyz$ for all nonnegatives $x,y,z$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_2788 (x y z : ℝ) (hx : 0 ≤ x) (hy : 0 ≤ y) (hz : 0 ≤ z) : x ^ 3 + y ^ 3 + z ^ 3 ≥ 3 * x * y * z   :=  by sorry

Source